Galvanotaxis assay for quantitative assessment of the metastatic potential of cancer cells

ABSTRACT

An apparatus and method for accelerating and/or inhibiting the migration of cells by applying a time-varying magnetic field to induce eddy currents that promote electrotaxis (galvanotaxis) of cells without the need for chemokines or glucose. The present invention can also be used to study and quantify the metastatic potential of different cell lines.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/826,487, filed Aug. 14, 2015, which is a continuation-in-part of U.S.application Ser. No. 14/765,993, filed Aug. 5, 2015, which is the U.S.national stage entry of International Application No. PCT/US14/14779,filed Feb. 5, 2014, which claims priority to U.S. ProvisionalApplication No. 61/760,987, filed on Feb. 5, 2013, each of which isherein incorporated by reference in its entirety.

BACKGROUND OF THE INVENTIVE FIELD

The present invention is directed to an apparatus and method ofaccelerating and/or inhibiting metastasis of cells by subjecting thecells to an electric field. More particularly, the present invention isdirected to an apparatus and method for accelerating and/or inhibitingmetastasis of cancer cells by applying a time-varying magnetic field toinduce electric fields that promote or hinder electrotaxis(galvanotaxis) of cells without the need for chemokines or glucose.

SUMMARY OF THE GENERAL INVENTIVE CONCEPT

In a preferred embodiment of the present invention, a time-varyingmagnetic field from an electromagnetic (EM) coil is used to induceelectric fields in a modified version of Corning's Transwelltransmembrane permeable assay. By varying the characteristics of theexcitation of the EM coil and the direction of application of theelectric field, it is possible to enhance cell migration as well ashinder it, in the presence or absence of chemokines. The modified assayprovides a novel method to study and quantify metastasis. For example,metastatic cell lines can be compared to each other in these assays bysubjecting them to the EM fields and counting the number of cells thatmigrate across the permeable membrane. Comparisons between cell linescan also be drawn and quantified in the presence of both EM fields andchemokines. Quantification can be accomplished by counting the cells orby digitizing the image and calculating cell coverage areas on thebottom of the membrane. In one embodiment, the EM coil is driven using afunction generator using a 20 Vpp, 100 kHz, sawtooth wave with a sharp˜50 ns drop to generate a rapidly time-varying magnetic field.

In an exemplary embodiment of the present invention, the method iscomprised of the steps of:

-   -   providing an electromagnetic coil having a first end and a        second end;    -   connecting the electromagnetic coil to a function generator;    -   applying a time-varying sawtooth voltage waveform to the        electromagnetic coil;    -   inducing a time-varying electric field around the        electromagnetic coil;    -   placing the electromagnetic coil adjacent to the location of        cancer cells with the direction of the induced electric field        directed towards the cancer cells;    -   orientating the placement of the electromagnetic coil so that        the direction of the electric field is directed away from an        area of healthy cells; and    -   hindering migration of the cancer cells using the induced        electric field.

In one embodiment the waveform applied to the coil is a 20 volts peak topeak, 100 kHz sawtooth waveform with a 50 ns drop off at its trailingedge that induces a rapidly time-varying magnetic field.

It is appreciated that the characteristics of the waveform can beadjusted to control metastasis.

Furthermore, the following additional steps may be taken according toone embodiment of the invention for studying and quantifying themetastatic potential of cell lines:

-   -   placing the electromagnetic coil in between a first row of a        plurality of assay wells and second row of a plurality of assay        wells;    -   providing a plurality of well inserts having a porous membrane;    -   placing one of the well inserts into each of the plurality of        assay wells so that the wells are divided into a lower and upper        compartment;    -   placing a medium into each of the plurality of assay wells;        placing a predetermined line of cancer cells into each of the        assay wells;    -   allowing the predetermined lines of cancer cells to settle on        top of the porous membranes;    -   taking an image of the porous membrane after the step of        inducing a time-varying electric field;    -   quantifying metastatic potential of the predetermined lines of        cancer cells; and    -   introducing a predetermined chemokine into each of the assay        wells.

The foregoing and other features and advantages of the present inventionwill be apparent from the following more detailed description of theparticular embodiments, as illustrated in the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The following detailed description of the example embodiments refers tothe accompanying figures that form a part thereof. The detaileddescription provides explanations by way of exemplary embodiments. It isto be understood that other embodiments may be used having mechanicaland electrical changes that incorporate the scope of the presentinvention without departing from the spirit of the invention.

In addition to the features mentioned above, other aspects of thepresent invention will be readily apparent from the followingdescriptions of the drawings and exemplary embodiments, wherein likereference numerals across the several views refer to identical orequivalent features, and wherein:

FIG. 1a illustrates an assay with an insert with a porous membrane;

FIG. 1b illustrates a top view of a modified transmembrane assay;

FIGS. 1c (top view), 1 d (front view), and 1 e (side view) illustrateone embodiment of the apparatus of the present invention having an EMcoil placed between two rows of wells;

FIG. 2a illustrates a sawtooth waveform applied to the coil in oneembodiment of the invention;

FIG. 2b illustrates a chart showing the induced electric fieldasymmetric over a duty cycle for one embodiment of the invention;

FIG. 2c illustrates a chart showing a induced electric field decreasingwith increasing radial distance from the outer surface of the coil forone embodiment of the invention;

FIGS. 2d and 2e illustrate charts showing contour charts of inducedelectric field for one embodiment of the invention;

FIG. 2f illustrates a chart showing cell migration based on inducedelectric field for one embodiment of the invention;

FIG. 3 illustrates a chart showing normalized percentage of cellsmigrated for one embodiment of the invention;

FIG. 4 illustrates the summary of results of SCP2 cell migration in amodified transmembrane assay showing the effects of induced E fieldswith and without chemokines/growth factors;

FIG. 5a illustrates one embodiment of an apparatus for visualizing actinfilaments under induced electric fields and results of experiments;

FIG. 5b illustrates the induced electric field versus time showing shapeof the field in 10 μs intervals;

FIG. 5c illustrates contours of induced electric field when viewed fromone end of the coil at the instant when the maximum induced E field is˜20 μV/cm;

FIG. 5d illustrates a contour plot of the induced E field at the bottomof the culture plate, at the instant when its maximum value is ˜20μV/cm;

FIG. 5e illustrates the variation of the induced E field versus (radial)distance away from the coil for one embodiment of the invention;

FIGS. 6a and 6b illustrate the visualization of actin filaments byfluorescence microscopy;

FIG. 7 illustrates one embodiment of a side-view of a glass welldepicting inserts;

FIG. 8 illustrates one embodiment of a holder of the present invention;

FIG. 9 illustrates one embodiment of representative fields (4 each) fromthe Transwell transmembrane assay and the modified transmembrane assaywith SCP2 cells fixed and stained showing how the cells are counted inone embodiment of the invention;

FIG. 10 illustrates how the modified transmembrane assay with theTranswell membrane inserts reproduces cell migration observed in themulti-well plates with the same inserts;

FIG. 11 illustrates one embodiment of a modified holder, coil, andculture plate used in the experiments to image actin filaments usingphalloidin and fluorescence microscopy;

FIG. 12 illustrates one embodiment of how a modified assembly foraccommodating a culture plate may be altered for a 96 well multi-wellplate;

FIG. 13 illustrates one embodiment of a circuit diagram showing the useof a sense resistor to measure the current through the coil;

FIG. 14 illustrates one embodiment of a circuit diagram showing a modelused to predict the current through the coil;

FIG. 15 illustrates a chart showing the total current through theelectromagnetic coil used in the transmembrane assay experimentsdiscussed herein;

FIG. 16 illustrates a chart showing predicted current (top) through theelectromagnetic coil used in the transmembrane assay experiments at aduty cycle of 100 kHz for a 20 Vpp sawtooth voltage waveform, and itsderivative (bottom);

FIG. 17 illustrates a chart showing predicted current through theelectromagnetic coil used in the actin filament imaging experiments, ata duty cycle of 100 kHz for a 20 Vpp sawtooth voltage waveform;

FIGS. 18a and 18b illustrate charts showing the average intensity ofactin fluorescence versus length along isolated cells shown in the leftpanel of FIG. 6 a;

FIGS. 19a and 19b illustrate charts showing the average intensity ofactin fluorescence versus length along isolated cells shown in themiddle panel of FIG. 6 a;

FIGS. 20a, 20b, and 20c illustrate charts showing the average intensityof actin fluorescence versus length along isolated cells shown in theright panel of FIG. 6 a;

FIG. 21 illustrates representative fields of view from the modifiedtransmembrane assay with a Transwell membrane with MCF-10A cells fixedand stained, showing how the cells are counted;

FIG. 22 illustrates a chart showing a summary of experimental results ofmigration of MCF-10A cells in the modified transmembrane assay showingthe effects of induced electric fields with and without the growthfactor EGF.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

An assay that is commonly used to evaluate the response of cancer cellsto chemokines and chemotherapy drugs is Corning's Transwell PermeableSupport assay 10. In this assay, inserts 12 with porous membranes 16 atthe bottom are placed into standard plate wells as shown in FIG. 1a .After coating the bottom of the membrane with fibronectin, and with asuitable chemokine placed in the lower compartment 18, a monolayer ofcells can be made to migrate from the upper compartment 14 to the lowercompartment. In other words, by placing suitable chemokines in the lowercompartment, the infiltration capabilities of cancer cells may bestudied by observing the number that migrate from the membrane side incontact with the upper compartment to the membrane side in contact withthe lower compartment. This is an example of chemotaxis, which refers tothe motility of cells under the action of a gradient in theconcentration of a chemical substance such as growth factors orchemokines. Biological cells move in response to other forces as well,such as electrical forces. The directional movement of biological cellsin the presence of an applied electric field is known as Galvanotaxis orelectrotaxis. This effect is named after Luigi Galvani, who in the18^(th) century discovered bioelectricity. The majority of experimentsrelated to galvanotaxis over the past two centuries have involved steadyelectric fields applied via electrodes placed in contact with the mediumcontaining cells (usually, the electrodes are in contact with the mediumcontaining the cells through agar filled tubes and the applied electricfield is usually DC).

The system and method of the present invention is used for inducingelectric fields in the medium containing cells, for example theCorning's Transwell permeable assay, by applying time-varying magneticfields. The method uses electromagnetic (EM) induction to induceelectric fields and eddy currents in the medium to promote or hindergalvanotaxis of cells without the need for chemokines or glucose.Hindrance is of significance since cancer cells are known to respond toexternally applied electric fields so that they can be distinguishedfrom normal cells. Moreover, metastatic potential of different cancercells may be quantitatively evaluated by counting the number of cellsmigrated across the membrane, so that this can form the basis for a newassay.

In one embodiment, a SCP2 cell line cultured in Dulbecco's ModifiedEagle Medium (DMEM) with a density of 3.3×10⁶ cells/mL is used. Thiscell line is a highly metastatic estrogen receptor (negative) breastcancer cell line derived from the MDA-MB-231 cell line. In thisembodiment, 150 μL of the medium containing this cell line (˜4.95×10⁴cells) is pipetted into the upper compartment of a single Transwellpermeable insert (equipped with a 6 μm filter) while the lowercompartment has 200 μL of the same medium but with no cells. The singleplate well with the insert is then placed adjacent to a horizontallyoriented electromagnetic (EM) coil (R ˜22Ω, L=10 mH) and fixture asshown in FIGS. 1c -1 e.

FIGS. 1c, 1d, and 1e illustrate schematics of one embodiment of theapparatus 20 of the present invention with modified Corning Transwellplates 22 with the electromagnetic (EM) coil 24 placed in the middle oftwo rows 25 of wells. These components are placed in a holder 26 asshown. The center line 28 of the coil is illustrated by the dashed lineas shown. The induced electric field is shown in FIG. 1d as the circledrawn around the coil. The glass wells are preferably configured withoffset holes to accommodate Corning Transwell permeable inserts withdimensions such that the centerline of the coil is at the same elevationas the membrane of the insert. FIG. 1c illustrates a top view of theapparatus. FIG. 1d illustrates a front view and FIG. 1e illustrates aside view. In another embodiment, a single well with one insert is used,adjacent to the coil. Once the cells are allowed to settle onto theupper surface of the permeable membrane (see FIG. 1a ), the entireapparatus is placed inside an incubator (at 37° C. with 5% CO₂) for aperiod of 12 hours. As control case, a similar plate well with similarpermeable insert and with the same highly metastatic cells, but notexposed to the EM coil, is also placed in the incubator. Both setups areimaged after a period of 12 hours.

In one embodiment, the EM coil is driven using a function generatorusing a 20 Vpp, 100 kHz, sawtooth wave with a sharp ˜50 ns drop togenerate a rapidly time-varying magnetic field with components B_(r) andB_(z). By Faraday's law these temporally varying magnetic fields fromthe EM coil induce an electric field E_(θ) in the medium containing thecells due to the small but non-zero electrical conductivity of themedium. Because of the placement of the plate well relative to the coil,this results in a vertically directed electric field across themembrane, but with E_(θ) decaying radially with increasing distance fromthe coil. At the driving frequency of 100 kHz, E_(θ) switches directionsback and forth (up and down) across the membrane, but with a componentdirected downward or upward for non-equal portions of a duty cycle,depending on the side of the coil.

Application of the time-varying magnetic field results in inducedelectric fields in the appropriate direction which increases migrationof the metastatic cancer cells across the membrane even in the absenceof chemokines. In contrast, the control case (with no applied electricfield) results in the typically observed random migration patterns. Byselecting a different set of characteristics for the driving waveform(e.g. waveform type, peak to peak voltage, and frequency) migration ofcells can be reduced by simply reversing the field. It should be notedthat this result is of significance for cancer treatment whereinhibition of metastasis in tumors may have beneficial effects in vivo.

In addition to implications for hindering metastasis, Corning'sTranswell assay can be modified to provide a method to quantifymetastasis. For instance, metastatic cell lines can be compared to eachother in these assays by subjecting them to the same EM fields andcounting the number of cells that migrate across the permeable membrane.The quantification can be accomplished by counting the cells or bydigitizing the image and calculating cell coverage areas on the bottomof the membrane. The effects of various drugs and chemokines may also beevaluated in the presence of EM fields so as to decipher the effects ofin vivo endogenous electric fields that may adversely affect thetherapeutic effects of chemotherapy drugs.

In summary, a time-varying magnetic field from an electromagnetic (EM)coil is used to induce electric fields in a modified version ofCorning's Transwell permeable assay. Preliminary in vitro experiments onthe highly metastatic SCP2 breast cancer cell lines show that cellmigration across the membrane can be significantly increased compared tothe control case where no EM field is applied. By varying thecharacteristics of the excitation of the EM coil, it is possible toaccelerate metastasis as well as hinder it. This degree of controlwithout the use of chemokines suggests a natural means of quantifyingthe metastatic potential of different cancer cells as well as a naturalmeans of comparing them with the motility of normal cells.

The present invention also relates to a method to induce electric fieldsand drive electrotaxis (galvanotaxis) without the need for electrodes tobe in contact with the media containing the cell cultures. The followingexperimental results were obtained using a modification of thetransmembrane assay, demonstrating the hindrance of migration of breastcancer cells (SCP₂) or (SCP2) when an induced a.c. electric field ispresent in the appropriate direction (i.e. in the direction ofmigration). Of significance is that migration of these cells is hinderedat electric field strengths many orders of magnitude (5 to 6) belowthose previously reported for d.c. electrotaxis, and even in thepresence of a chemokine (SDF-1α) or a growth factor (EGF).

Induced a.c. electric fields applied in the direction of migration arealso shown to hinder motility of non-transformed human mammaryepithelial cells (MCF₁₀A) or (MCF10A) in the presence of the growthfactor EGF. In addition, as discussed below, the method of the presentinvention can be applied to other cell migration assays (scratch assay).Furthermore, the present invention demonstrates that by changing thecoil design and holder, the method is also compatible with commerciallyavailable multi-well culture plates.

Cell migration is important in several physiologically relevantsituations such as embryonic development, wound healing, and metastasisof cancer. Non-ciliated cells migrate in response to gradients inchemical composition (chemotaxis), mechanical forces, and electricfields (galvanotaxis or electrotaxis). The latter has been observed forover a hundred years since the report of Dineur in 1892, where theauthor proposed the use of the term galvanotaxis to describe migrationof leukocytes in the presence of a d.c. electric field.

Since Dineur's report, many vertebrate cells have been observed toexhibit galvanotaxis or electrotaxis as it is now called. The majorityof in vitro electrotaxis experiments are conducted under the action of ad.c. field, and involve metal electrodes directly inserted into themedium containing the cells or in indirect contact through agar or saltbridges. The threshold for cells to sense an electric field in vitro hasbeen reported to be >10 mV/cm, with magnitudes of d.c. electric fieldson the order of 0.1-10 V/cm required for observing electrotaxis. Atthese electric field strengths, effects of localized heating can benon-negligible.

Recently, electrotaxis experiments in a.c. fields of very lowfrequencies on the order of mHz, and a.c. fields from 1.6 Hz to 160 Hzapplied together with d.c. fields have been reported. These experimentsshow that collective cell migration, direction of cell migration andmigration speed can all be controlled by application of electric fields.Despite the use of modern patterning techniques for shaping d.c.electric fields and use of microfluidic devices, the methods of applyingthese d.c. and very low-frequency a.c. electric fields still involveeither direct contact or indirect contact (via agar bridges) with themedia containing the cells. Since the methods of applying electricfields have changed little over the past several decades, there is aneed for new electrotaxis assays and methods of applying electric fieldsin a non-contact manner.

As described herein, a well-known assay for chemotaxis referred to asthe transmembrane or Transwell assay may be modified to conductnon-contact electrotaxis experiments. The transmembrane assay was firstdescribed by Boyden to analyze the chemotactic response of leukocytesand is sometimes referred to as the Boyden chamber assay. This assayconsists of an insert at the bottom of which is a membrane of selectablepore size (0.4 μm-12 μm), depending on the size of the cells. The insertis then placed into a well, forming two distinct compartments separatedby the membrane. Cells are seeded on the top side of the membrane, andthe bottom compartment may contain a chemotactic agent. The cellsmigrate from the top surface of the membrane through to the bottomsurface. After a suitable incubation time (dependent on cell type), thenumber of migrated cells is counted by fixing and staining, or bystaining fluorescently, removing from the membrane by dissociation (e.g.by using trypsin) and using a fluorescent reader.

The standard transmembrane assay may be modified to develop a new methodfor inducing a.c. electrotaxis in a truly non-contact manner, withoutthe need for electrodes and agar or salt bridges to be in contact withthe medium containing the cells. Moreover, this new system and methodenables the study of electrotactic behavior alone or electrotaxis in thepresence of chemotactic agents as well. The a.c. electric fields areinduced in the media containing the cells using electromagneticinduction. A time-varying current driven through a custom designed coilplaced with glass wells (with membrane inserts) lining either side ofthe coil enable an electric field to be induced in the verticaldirection, along the axis of migration. The time-varying currentgenerates a time-varying magnetic field which induces an electric fieldin the azimuthal direction around the coil. When the glass wellscontaining the membrane inserts are placed on the sides of the coil,this azimuthal field is in the direction perpendicular to the membranesand along the axis of migration. Results are presented for a highlymetastatic human breast cancer cell line as well as for anon-transformed human mammary epithelial cell line (MCF₁₀A) (FIGS.21-22), for a single duty cycle of 100 kHz as illustrative examples. Themodification of the method can induce electric fields in a non-contactmanner in standard culture plate wells, enabling visualization of actinfilaments using phalloidin-fluorophore conjugates and fluorescencemicroscopy, and extending applicability of this method to the scratchmigration assay as well.

FIGS. 1c-1e illustrate one embodiment of a transmembrane assay modifiedto incorporate an electromagnetic (EM) coil to induce electric fields todrive electrotaxis. FIG. 1c illustrates a top view of the modifiedtransmembrane assay showing the custom-made glass wells, 3D printedholder apparatus, and an EM coil. (FIGS. 1c-e ). Schematics showing thetop, front, and side views of the modified transmembrane assay includingEM coil and glass wells custom-made to incorporate commerciallyavailable Transwell membrane inserts. Also shown in the front view ofthe apparatus is the direction of the induced electric field appliedover a majority (60%) of the 10 μs period.

Using the present invention, it was determined that weak a.c. electricfields hinder migration of highly metastatic SCP₂ cells. In oneembodiment, the experimental apparatus was comprised of a EM coil,holder, glass wells that can accommodate commercially availableTranswell permeable inserts (e.g., 8 μm pore, 24-well, Corning-Costar,Lowell, Mass.), and a function generator (Hewlett Packard 33120A). Inthis embodiment, the coil has a d.c. resistance of 50.45Ω, and aninductance of 14.25 mH as measured by an LCR meter (Extech InstrumentsModel 380193) at 1 kHz. The coil is placed at the center of the holderwith six glass wells on either side (FIGS. 1c-1e , FIGS. 7-8). The glasswells preferably have off-centered holes within which commerciallyavailable Transwell membrane inserts can be placed at closest proximityto the coil (FIGS. 1c-1e , FIG. 7). The wells and holder are designedand fabricated so that each membrane of the transmembrane insert ispositioned at the same height as the centerline of the coil. One side ofthe coil is arbitrarily labeled “North” for ease of reference while theother is labeled “South”, with respect to the red wire labeled “East”.

Highly metastatic breast cancer cells known as SCP₂, a single cellpopulation derived from MDA-MB-231 that is known to metastasize to thebone, were cultured in Dulbecco's Modified Eagle Medium (DMEM; LifeTechnologies, Gaithersburg, Md., USA), supplemented with 10% heatinactivated fetal bovine serum (FBS), 5 U/mL penicillin, and 5 mg/mLstreptomycin. The SCP₂ cells were placed in the upper chamber, and bothcompartments contained 0.1% FBS-DM. The entire apparatus (holder, coil,modified transmembrane chambers with Transwell inserts and cells) wasplaced in a 37° C. culture incubator with humidified air containing 5%CO₂. The leads of the coil were connected to the function generatorplaced outside the incubator. The cells were allowed to migrate for 8hours, and then were fixed and stained using Hema-3 stain kit accordingto the manufacturer's instructions. The number of migratory cells permembrane was then measured using light microscopy by counting the totalnumber of cells in each of five contiguous images spanning radiallyoutward (five fields) from the coil (FIG. 9). The counts were used todetermine the normalized percentage of migration, with the number ofcells migrated in the control set to 100%. In order to ensure that cellmigration in the modified transmem-brane assay with the Transwell insertis not statistically different from the conventional transmembraneassay, control experiments were performed (FIG. 10).

In one embodiment, a 20 Vpp, 100 kHz sawtooth shaped voltage waveform(FIG. 2a ) was imposed on the coil, resulting in a time-varying currentflow generating a time-varying magnetic field. In accordance withFaraday's Law, the time-varying magnetic field induces an electricfield. This induced electric field can be calculated and is in theazimuthal direction (vertically up or down with respect to the membraneinserts). The induced electric field is asymmetric over a duty cycle(FIG. 2b ), resulting in different durations of the electric field inthe direction of migration on the two sides of the coil. On the side ofthe coil labeled “North”, the induced electric field is in the directionof migration (i.e. downward) over ˜60% of a single duty cycle lasting 10μs with a maximum magnitude of ˜2.3-2.4 μV/cm (FIG. 2b-2e ). Over theremaining 40% of the 10 μs period, the induced electric field on the“North” side is in the direction opposite to that of migration (i.e.upward) with a maximum magnitude of ˜(−)3.7-(−)3.8 μV/cm (FIG. 2b-2e ).The opposite of these trends is realized on the side labeled “South”. Atany instant of time, the induced electric field decreases withincreasing radial distance from the outer surface of the coil (FIG. 2c). Contours of the calculated induced electric field reveal that it isfairly uniform over the length of the coil so that each of the threewells on a given side of the coil experiences the same induced electricfields at a given instant of time (FIGS. 2d and 2e ). In thisembodiment, the maximum induced electric fields are on the order of ˜3.8μV/cm, at least four to five orders of magnitude smaller than typicallyrequired for electrotaxis and six orders of magnitude smaller thanpreviously reported for MDA-MB-231 cells.

Experimental results with SCP2 cells indicate that migration on the“North” side of the coil is hindered (p=0.021) when compared to thecontrol experiments where no electric field is present. However,migration on the “South” side of the coil shows a trend of increasedmigration which is not statistically significant (p=0.076) when comparedto the controls where no electric field is present (FIG. 2f ). Since the“North” side of the coil experiences an electric field in the directionof migration (i.e. downward) for a greater duration (˜6 μs per period)compared to experiencing an electric field opposite to the direction ofmigration (˜4 μs per period), it can be seen that migration of SCP2cells is hindered when the induced electric field (across the membrane)is in the direction of migration. This observed hindrance of migrationon the “North” side is consistent with previously reported observationsthat MDA-MB-231 cells migrate toward the positive electrode whensubjected to d.c. electric fields.

FIG. 2a illustrates one embodiment of a sawtooth shaped voltage waveformoutput from the function generator used to drive current through the EMcoil. The sharp drop-off occurs in ˜50 ns. FIG. 2b illustrates the timevariation of the induced azimuthal electric field E_(θ) calculated fromfirst principles (see e.g., FIGS. 13-17), for all wells in the describedembodiment. This induced E field is in the vertical direction (up ordown) at the membrane inserts placed on either side of the coil. In thisembodiment, the asymmetry over a given 10 μs interval (positive ˜60% ofthe time and negative ˜40% of the time over the interval). Based on thedirection of the windings of the coils in this embodiment, a positiveE_(θ) indicates that the induced E field is in the downward direction onthe “North” side of the coil while a negative E_(θ) indicates anupwardly directed induced E field on the “North” side of the coil. FIG.2c illustrates variation of the maximum E_(θ) versus radial distanceaway from the coil (i.e. along the porous membrane) calculated for eachaxial location where the glass wells are placed. FIG. 2d illustrates acontour plot of the induced E field on both sides of the coil where thewells are placed, for ˜60% of each 10 μs period. FIG. 2e illustrates acontour plot of the induced E field on both sides of the coil, for ˜40%of each 10 μs period. FIG. 2f illustrates results showing effects ofinduced E fields on migration of SCP2 cells (N=3). In this embodiment,the migration is hindered on the “North” side of the coil (p=0.021)while it follows a weak trend of enhanced migration on the “South” sidewith a borderline non-significant p value (p=0.076). The induced E fieldis directed downward (in the direction of migration) for ˜60% per periodwhile it is directed upward (against the direction of migration) for˜40% per period on the “North” side of the coil. These values arereversed for the “South” side of the coil.

Effects of hindered migration of SCP2 cells under weak a.c. fields arereversible. The observed hindrance of migration of SCP2 cells under theaction of weak (˜1 μV/cm) induced electric fields raises the question ofwhether or not the ability of these cells to migrate is permanentlyaffected after exposure to the induced electric field. In order toaddress this question, SCP2 cells were prepared as described before, in0.1% serum media and control experiments were separately conducted inthe modified trans-membrane assay without application of the inducedelectric field, for 8 hours and 16 hours respectively (8 hr control (1)and 16 hrs control (4), FIG. 3). In parallel, SCP2 cells were subjectedto an induced electric field generated by a sawtooth voltage waveform at20 Vpp and 100 kHz duty cycle on the “North” side of the coil for 8hours (8 hrs+E (2), FIG. 3, p<0.001 for 8 hrs control (1) and 8 hrs+E(2)) and a separate set which were subjected to the electric field(“North” side) for 8 hours after which time the electric field wasturned off and migration allowed to continue for another 8 hours (8hrs+E 8 hrs−E (3), FIG. 3, p<0.001 for 8 hrs control (1) and 8 hrs+E 8hrs−E (3)). It can be seen from these results that as discussed before(FIG. 2f ), application of the induced electric field in the directionof migration hinders SCP2 cell movement (8 hrs control (1) versus 8hrs+E (2), FIG. 3).

However, once the electric field is turned off after 8 hours, it can beseen that the SCP2 cells migrate over the next 8 hours in numberscomparable to the corresponding control case (8 hrs+E 8 hrs−E (3) versus16 hrs control (4), FIG. 3, p=0.342 for 8 hrs+E 8 hrs−E (3) and 16 hrscontrol (4)). Furthermore, migration when exposed to the inducedelectric field for 16 hours is hindered compared to both the control (noinduced electric field for 16 hours) and the case where the inducedelectric field is shut off after 8 hours (16 hrs+E (5) versus 8 hrs+E 8hrs−E (3) or 16 hrs control (4), FIG. 3). These results show that themigration properties of the SCP2 cells are not irreversibly altered bythe application of an induced electric field, and that the effects ofelectrotaxis are reversible once the induced electric field is turnedoff (8 hrs+E (2) and 8 hrs+E 8 hrs−E (3) versus 16 hrs control (4), FIG.3).

FIG. 3 illustrates the results showing the effects of turning off theinduced electric field on SCP2 cells on the “North” side of the coilafter cells have been exposed to it for 8 hours. As indicated in thechart of FIG. 3: 8 hrs control (1): Control experiments used fornormalization, showing cells migrated in 0.1% serum media after 8 hourswith no induced E field, as 100%. 8 hrs+E (2): Hindered migration(consistent with FIG. 2f ) of SCP2 cells in the presence of an induced Efield (8 hrs control (1) and 8 hrs+E (2): p<0.001). 8 hrs+E 8 hrs−E (3):Migration of cells after 16 hours, with the induced E field for thefirst eight hours and the field shut off for the next 8 hours (8 hrscontrol (1) and 8 hrs+E 8 hrs−E (3): p<0.001). 16 hrs control (4):Control experiments showing cell migration after 16 hours with noinduced E field. In this embodiment, cell migration appears to berestored to normal levels despite hindered migration of SCP2 cells dueto the induced E field for the first 8 hours (8 hrs+E 8 hrs−E (3) and 16hrs control (4): p=0.342). 16 hrs+E (5): Migration of cells after 16hours in the presence of an induced E field (16 hrs control (4) and 16hrs+E (5): p<0.001).

Weak a.c. electric fields hinder chemotaxis of metastatic breast cancercells. Experiments on combined chemotaxis and electrotaxis were alsoperformed with the SCP2 cells on the modified trans-membrane assay inorder to examine the effects of the induced a.c. electric field inhindering chemotaxis. Two well-known chemokines/growth factors to whichSCP2 cells respond, stromal-derived factor 1-α (SDF-1α), also known asCXCL12, and epidermal growth factor (EGF), were selected forinvestigation and placed in the bottom compartment of the custom-madechamber of the modified transmembrane assay. CXCR4 is a receptor that isoverexpressed in malignant breast cancer, and is known to bind to itscognate ligand CXCL12 (SDF-1α) and has been correlated with poorprognosis. EGF is known to be a growth factor that causes leading edgeprotrusions, an early event in migration of breast cancer cells. CXCR4positive breast cancer cells have been shown to metastasize to CXCL12expressing organs as their first destination. It has also been reportedthat CXCL12/CXCR4 signaling induces actin polymerization and chemotacticproperty of breast cancer cells. Both SDF-1α and EGF are also well knownto initiate chemotaxis of breast cancer cells in the transmembranemigration assay. In these experiments, the induced a.c. electric fieldwas produced by applying the same 20 Vpp, 100 kHz sawtooth shapedvoltage waveform described earlier (FIG. 2a ).

Using the system and methods of the present invention, it was determinedthat even in the presence of chemokines/growth factors such as SDF-1αand EGF, the induced electric fields on the “North” side hindermigration of SCP2 cells relative to migration levels without the field(SDF control versus SDF North, p=0.001; and EGF control versus EGFNorth, p=0.001, FIG. 4). Chemotaxis control experiments were alsoperformed separately with chemokine SDF-1a (Control ver-sus SDF control,FIG. 4, p=0.015) and growth factor EGF (Control versus EGF control, FIG.4, p=0.001). Several key observations are immediately evident from theseresults (FIG. 4). First, chemotaxis is well enabled in the presence ofchemokine SDF-1α and growth factor EGF in the modified transmembraneassay. Second, even in the presence of this chemokine and growth factor,the weak induced electric field applied in the direction of migrationsuccessfully hinders the migration of SCP2 cells compared to thecorresponding cases of chemotaxis in the presence of SDF-1α or EGFalone. This is a significant result since recent works have shown thatdisruption of the SDF-1α signaling pathway can prevent metastasis andimprove the ability of other treatment modalities (radiation orchemotherapy) to attack the tumor.

FIG. 4 illustrates the summary of results of SCP2 cell migration in amodified transmembrane assay showing the effects of induced E fieldswith and without chemokines/growth factors (SDF-1α or EGF) after 8 hours(N=3). Inset shows schematic end view of apparatus showing the directionof the induced field for ˜60% of the 10 μs period. In this embodiment,the function generator drives the coil with a 20 Vpp sawtooth shapedvoltage transient at 100 kHz duty cycle. Control: Control withoutinduced E fields or chemokines/growth factors in the modifiedtransmembrane assay. SDF control: Control in the modified transmembraneassay with a Transwell insert, without induced E fields but in thepresence of chemokine SDF-1α in the lower chamber (Control vs. SDFcontrol: p=0.015). SDF North: Migration is hindered on the “North” sideof the coil, where for the majority (60%) of the 10 μs period, theinduced E field is in the direction of migration (i.e., directeddownward), even in the presence of the chemokine SDF-1α (SDF control vs.SDF North: p=0.001). EGF control: Control in the modified transmembraneassay with a Transwell insert, without induced E fields but in thepresence of growth factor EGF in the lower chamber (Control vs. EGFcontrol: p=0.001). EGF North: Migration is hindered (relative to thecase where there is no E field) on the “North” side of the coil, wherefor the majority (60%) of the 10 μs period, the induced E field is inthe direction of migration (i.e., directed downward), in the presence ofgrowth factor EGF (EGF control vs. EGF North: p=0.001).

The apparatus of the present invention enables visualization of actinfilaments under induced electric fields. The actin cytoskeleton is knownto play an important role in cell migration, especially in transmittingforce through adhesion complexes to the substrate. Visualization ofactin filaments can therefore help identify so called leader cells andexpose any effects of induced electric fields on the internal cellmachinery involved in migration. In aid of observing the actincytoskeleton, a separate holder assembly (FIG. 5a , FIG. 11) can beconstructed to orient an electromagnetic coil in such a way as to placea single-well culture plate or a multi-well culture plate on top of ahorizontal coil (FIG. 12). In such a configuration, the induced electricfield can be calculated for the 20 Vpp, 100 kHz saw-tooth shaped voltagewaveform discussed here (FIGS. 5b-5d ). Depending on the coil diameter,shape and size, the field can be made uniform over a desired region ofthe culture plate. This method is particularly well suited to being usedin conjunction with the scratch assay.

The present invention allows the visualization of actin filaments thatform the cytoskeleton of the SCP2 cells and play a crucial role in cellmigration, when induced electric fields are applied in a non-contactmanner as described earlier (FIG. 6). The images are quantified todetermine the actin filament distribution within the cell as representedby the fluorescence intensity. In one embodiment, SCP2 cells are platedon a single-well, 60 mm diameter culture plate, allowed to migratefreely for an hour, and then fixed and stained withphalloidin-fluorophore conjugate for visualization of the actinfilaments (FIG. 6a , left panel). SCP2 cells were incubated with EGF forone hour in the presence and absence of induced electric fields and theactin filaments stained with phalloidin-fluorophore conjugate werevisualized by confocal microscopy (FIG. 6a , middle and right panels).These images have also been quantified after importing into MATLAB(FIGS. 18-20). In the control case (no electric field and no chemokine),there is little visible polymerization of actin filaments and nodiscernible preferential direction of formation of filopodia (FIG. 6aleft panel, FIG. 18a-b ). In contrast, in the presence of the growthfactor EGF, polymerization of actin filaments can be observed at one endof some cells (FIG. 6a middle panel, FIG. 19a-b ). When an electricfield is induced in the presence of EGF, actin polymerization can beseen throughout the cells with no preferential direction and whichinhibits formation of filopodia (FIG. 6a right panel, FIGS. 20a-20c ).These effects are also apparent when a contiguous layer of SCP2 cells isformed (FIG. 6b ). The so-called “leader” cells at the edge of thecontiguous layer can be seen to respond to the growth factor EGF (FIG.6b , left), while in the presence of both EGF and the induced electricfield, no directional polymerization of actin is evident (FIG. 6b ,right panel).

FIG. 5 illustrates one embodiment of an apparatus for visualizing actinfilaments under induced electric fields and results of experiments. Inthis embodiment, the current through the coil is driven by a 20 Vppsawtooth shaped voltage waveform at 100 kHz duty cycle. The apparatus isshown with the coil used in actin imaging experiments, in a 3-D printedholder and placed underneath a culture plate. FIG. 5b illustrates theinduced electric field versus time showing shape of the field in 10 μsintervals. Note that this coil design yields maximum electric fieldstrengths of ˜20 μV/cm, and is approximately symmetric within the 10 μsperiod (i.e. on for equal duration leftward and rightward). FIG. 5cillustrates contours of induced electric field when viewed from one endof the coil at the instant when the maximum induced E field is ˜20μV/cm. FIG. 5d illustrates a contour plot of the induced E field at thebottom of the culture plate, at the instant when its maximum value is˜20 μV/cm. Note that the induced E field is fairly uniform spatiallyover a region approximately 1 cm×1 cm. Cells are typically plated in thecenter of the plate. FIG. 5e illustrates the variation of the induced Efield versus (radial) distance away from the coil, at the instant whereits maximum value is ˜20 μV/cm. Since the thickness of the bottom ofculture plates is typically ˜1 mm, it is important to keep thisvariation in mind as one designs coils to exert a particular value ofthe induced E field at specific locations of a culture plate.

FIG. 6 illustrates the visualization of actin filaments by fluorescencemicroscopy. FIG. 6a (left panel) actin cytoskeleton in SCP2 cells in theabsence of both EGF and induced electric fields. FIG. 6a (center panel)actin cytoskeleton in SCP2 cells in the presence of the growth factorEGF. The white arrows indicate regions of polymerization of actinfilaments signifying cellular movement or preparation for movement inresponse to the growth factor. FIG. 6a (right panel) actin cytoskeletonin SCP2 cells in the presence of EGF and an induced electric field. Notethe polymerization of actin filaments within the cell filopodia in thecenter panel (indicated by white arrows) which are absent in the leftand right panels. In the presence of the induced electric field, thereis no preferential direction in the formation of the actin bundles.

FIG. 6b (left panel) illustrates the edge of a contiguous layer of SCP2cells in the presence of EGF, showing actin polymerization (indicated bywhite arrows) in some cells (so called “leader” cells) as they migrateor prepare to migrate. FIG. 6b (right panel) illustrates the edge of acontiguous layer of SCP2 cells in the presence of EGF and inducedelectric fields. Note there is no preferential direction for formationof actin bundles. Green and red represent F-actin and nucleus staining,respectively, where the F-actin is detected phalloidin-fluorphore (AlexaFluor 568) conjugate.

Weak a.c. electric fields hinder chemotaxis of “normal” breastepithelial cells. Experiments on combined chemotaxis and electrotaxiswere performed with MCF10A cells in the same modified transmembraneassay in order to examine the effects of the induced a.c. electric fieldin hindering chemotaxis of non-transformed cells. MCF-10A cells are anon-transformed epithelial cell line derived from human fibrocysticmammary tissue. These cells are considered “normal” breast epithelialcells as they have a karyotype that is nearly diploid, are dependent onexternally supplied growth factors for migration, and lack the abilityto form tumors in nude mice. The growth factor EGF was used as anexogenous agent to induce MCF-10A cells to migrate in the modifiedtransmembrane assay, as in the case of the SCP2 cells. No migration ofMCF-10A cells was observed without EGF in the bottom chamber. As in theprevious experiments with SCP2 cells, the induced a.c. electric fieldwas produced by applying the same 20 Vpp, 100 kHz sawtooth shapedvoltage waveform (FIG. 2a ). Results with the induced electric field andin the presence of EGF were then compared to those of the control casesin the presence of EGF and no induced electric field.

The experimental results with the MCF-10A cells are summarized in FIGS.S15-S16. It can be seen that the MCF-10A cells do not migrate withoutthe presence of the growth factor EGF. Furthermore, the induced electricfields on the “North” side hinder migration of MCF-10A cells relative tomigration levels without the field in the presence of EGF (CoilNorth+E+EGF (4) versus−E+EGF (3), p=0.002; FIG. 22). In contrast,induced electric fields on the “South” side do not affect MCF-10A cellmigration in a statistically significant manner (data not shown).

The present invention includes a method for inducing electric fields byelectromagnetic induction (according to Faraday's Law) and drivingelectrotaxis without the need for electrodes in contact with the mediacontaining cell cultures. This method has been applied and demonstratedon the modified transmembrane assay commonly used for studyingchemotaxis. The modification to the existing transmembrane assayconsists of glass wells (FIG. 1, FIG. 7) that are designed toincorporate commercially available membrane inserts, placed on eitherside of an in-house designed and fabricated coil (FIG. 1a ), and placedon a holder that is fabricated using 3-D printing technology (FIG. S2).The method can be applied to other cell migration assays such as thescratch assay. By changing the length and diameter of the coil andassociated holder, the method is also compatible with commerciallyavailable multi-well culture plates (FIG. S6).

Experiments in the modified transmembrane assay using a single cellpopulation SCP2 isolated from the MDA-MB-231 breast cancer cell lineshow that application of weak induced electric fields (on the order of˜1 μV/cm) is able to mitigate normal migration of these cells when theelectric field is applied in the direction of migration. Moreover, SCP2cell migration is also hindered in the presence of these weak a.c.induced electric fields, in the presence of the well-known chemokineSDF-1α and growth factor EGF. This is the first time that such low-levelelectric fields (as low as six orders of magnitude smaller thanpreviously reported) have been shown to have an effect on electrotaxis.No negative effects of the induced electric fields on the cells havebeen observed. In fact, experiments in which the induced electric fieldwas applied for 8 hours to hinder SCP2 cell migration revealed that thecells continued to migrate normally when the electric field was shutoff.

Experiments have also been performed on the non-transformed humanmammary epithelial cells MCF-10A in the modified transmembrane assay.These cells do not normally migrate unless growth factors are externallysupplied. Results from these experiments also show that application ofweak induced electric fields is able to hinder their migration in thepresence of growth factor EGF and when the field is applied in thedirection of migration. These experiments show that the platform forapplying induced electric fields presented here is applicable todifferent cell lines, both non-transformed and transformed. Theusefulness of the present method may extend beyond using the modifiedtrans-membrane assay for quantifying the degree of metastasis of aparticular cell line, or for studying electrotaxis when subjected to ana.c. field in a non-contact manner and in the presence of chemokines.The non-contact manner in which the E-field is applied may be useful ininhibiting metastasis, or in orchestrating wound healing in vivo. Byvarying the direction and spatial extent of the induced electric field,the approach presented here can enable different cells (e.g.keratinocytes, fibroblasts, endothelial cells, and macrophages) tomigrate at different times during the wound healing process resulting inaccelerated healing beyond just the superficial layers. Application ofelectric fields over periods of hours and days is also physiologicallyrelevant in the treatment of cancers. So called tumor treating fields(TTF) have been successfully used to treat recurrent glioblastoma (GBM)and extend patient survival. While the mechanism of action of TTFs maybe different than the method presented here (the induced a.c. electricfields in this work are up to six orders of magnitude smaller), cellmigration may be affected in both approaches. By combining the abilityto simultaneously study chemotaxis and electrotaxis using the modifiedtransmembrane assay, new combinations of treatment strategies and drugsmay be identified or ruled out earlier in the drug discovery screeningprocess by revealing undesirable effects.

In one embodiment, the custom made glass wells are only identical indimension up to fractions of a millimeter (FIG. 7). Consequently, theholder is preferably designed using computer-aided design (CAD) methodsand fabricated after the glass wells have been made. Once the dimensionsof the glass wells have been determined (FIG. 7), a CAD drawing isdeveloped using the commercially available software SolidWorks (FIG. 8).The holder is then printed using plastic material according to thespecifications on the CAD drawing on a 3D printer (Stratasys Fortus 400MC). Since the outer radius of the coil may vary along its length due tounevenness of the windings, it is recommended that the middle channelwhere the coil is to reside be made of the smallest outer diameter ofthe coil so that specific locations in the channel may be groundmanually to ensure that the coil fits in the center channel properly.The depth of each well in the holder is designed so as to ensure thatthe membrane is positioned exactly at the height corresponding to thecenterline of the coil (FIGS. 1b-1e ).

Fabrication of the coil for the modified transmembrane assayexperiments: The electromagnetic coil used to generate the inducedelectric fields across the transmembrane inserts is comprised ofmultiple windings (35 layers, ˜159 turns per layer) of insulated 32 AWG(0.268 mm diameter with insulation or 0.202 mm diameter bare) wire woundaround a glass rod. The inner diameter of the coil is 3 mm, the outerdiameter is 1.4 cm, and its length is 10.5 cm. The coil resistance andinductance were measured using an LCR meter (Extech Instruments Model380193) to be 50.45Ω and 14.25 mH, respectively, at 1 kHz. The coil isplaced at the center of the holder (FIG. 8) with six glass wells oneither side. The wire gage, inner and outer diameters, number of turns,length, and number of layers in the coil can be varied depending on thetype of experiment to be conducted. The duty cycle of the imposedvoltage (which is 100 kHz for the results presented here) and itsmagnitude can also be easily changed. It is important to ensure that thefunction generator (Hewlett Packard 33120A 15 MHz in the presentexperiments) is able to drive sufficient current through the coil.

Fabrication of custom glass wells to accommodate transmembrane inserts,analysis of induced electric fields in modified transmembrane assayexperiments, analysis of induced electric fields in visualization ofactin filaments, and supple-mental data on migration of MCF-10A cellswith and without growth factor EGF and with and without induced electricfields, are described in more detail below.

In one embodiment, low passage SCP2 cells were cultured in Dulbecco'sModified Eagle's Media (DMEM) containing 10% fetal bovine serum (FBS)and 5 U/mL penicillin, and 5 mg/mL streptomycin at 37° C. in ahumidified culture incubator supplied with 5% CO₂. To perform cellmigration and actin filament imaging experiments, SCP2 cells were washedwith serum free media three times and incubated with 0.1% FBS-DMEM mediafor six hours. The cells were detached from the culture plates byincubating in 1 mL of trypsin-EDTA for 2-4 min. The trypsin wasneutralized by adding 2 mL of 0.1% FBS-DMEM. The cells were centrifugedat 1200 rpm for five minutes and re-suspended in 1 mL of 0.1% FBS-DMEM.The cells were counted using a hemocytometer. 1.5×10⁵ cells in 150 μL ofmedia were placed in the top chamber of the modified transmembraneassay. The bottom chamber was filled with 600 μL of 0.1% FBS-DMEM withor without 100 ng/mL of chemokine (SDF-1α) or growth factor (EGF). Afterallowing 8 or 16 hours of incubation in the modified transmembraneassay, the cells that migrated to the other side of the Transwellmembrane in the top chamber were stained with Hema 3 stain kit (FisherScientific, 122-911) according to the manufacturer's instructions. Thestained cells were then photographed with a Zeiss microscope attached toa camera. The migrated cells were counted in five representative fields.As an illustration, four representative fields for a control case and acase with the induced electric field are shown in FIG. 9.

In one embodiment, MCF10A cells were cultured in Dulbecco's ModifiedEagle's Media (DMEM) F12 containing 5% horse serum (HS), 20 ng/mlepidermal growth factor (EGF), 0.5 mg/ml hydrocortisone, 100 ng/mlcholrea toxin, 10 μg/ml insulin and 5 U/mL penicillin, and 5 mg/mLstreptomycin at 37° C. in a humidified culture incubator supplied with5% CO₂. MCF10A cells were prepared for migration assay using 0.1%HS-DMEM-F12 media as described above. 1.5×10⁵ cells in 150 μL of mediawere placed in the top chamber of the modified transmembrane assay. Thebottom chamber was filled with 600 μL of 0.1% HS-DMEM-F12 with orwithout 50 ng/mL EGF. After allowing migration for 16 hours, cells werestained, photographed and counted as described for the preparation ofthe SCP2 cells.

For the actin imaging experiments, the SCP2 cells were cultured in 60 mmculture dishes (Falcon, 353001) overnight in 10% FBS-DMEM andsubsequently incubated in 0.1% FBS-DMEM for at least six hours. Inanother experiment to make a contiguous layer of cells, a straight wound(scratch) was created by the tip of 200 μL pipette tip. The simulatedwound was aligned on top of the coil axis to observe the effects of theinduced electric field on EGF-induced actin polymerization.

The cells were incubated in EGF (100 ng/mL) for one hour in the presenceor absence of an induced electric field. Subsequently, the cells werewashed with ice cold PBS and fixed with 4% paraformaldehyde. Further,the cells were permeabilized by 0.1% triton X-100 for 15 min and stainedwith Phalloidin conjugated with the fluorophore Alexa Fluor 568 (1:300×)(Molecular Probes) for one hour. Finally, the cells were mounted withVECTASHIELD hard set mounting media with DAPI (Vector labs) andvisualized using an Olympus FV1000 confocal microscope.

To achieve statistical significance, in some cases three independentexperiments consisting of three wells each were performed andrepresentative data presented. In other cases, two independentexperiments consisting of two wells were performed. The data werecomputed as mean±SD. Group means were compared by using the Student ttest and p<0.05 was considered as significant. Statistical analysis wasperformed with Microsoft excel (Microsoft Corporations, USA).Statistical significance is denoted in the figures by ‘*’ (0.01≤p<0.05),‘**’ (0.001≤p<0.01), and ‘***’ (p<0.001). Where sample sizes (N) areindicated, these denote results from independent experiments. Forexample, N=3 refers to three independent experiments measuring migrationon for example the “North” and includes the three wells on that side ofthe coil.

Fabrication of custom glass wells to accommodate transmembrane inserts:in one embodiment, the glass wells (FIG. 1b-e and FIG. 7) in which thetransmembrane inserts can be placed were made from 14.6 mm I.D.×17 mmO.D. borosilicate glass tubing (C.O.E. 32×10⁻⁷). Using a fixed carbonroller adjusted to an angle of 120 degrees to the glass tubing as itturned being chucked in a lathe, a hand torch heated the material untila suitable working state of the glass was reached. Air was introducedthrough the center of the closed end tube, expanding the molten materialuntil it made contact with the graphite roller. The roller shaped thematerial into the desired conical shape, leaving a tubular opening oneach end to be closed later. Following formation of the well shape, thelarger end was closed and shaped flat, this surface being perpendicularto the wall of the stock tubing. The finished end was then fixed intothe tail chuck of the glass working lathe to allow the part to betemporarily separated from the stock material from which it had beenformed. The stock material was closed flat and perpendicular to itswall, leaving only a small opening in the form of a tabulation shape, toallow for expanding air inside the well to escape as the part was sized.The lower portion was finished to measure approximately 9 mm in lengthfrom the closed bottom up to the point where its diameter began toexpand into the shape of a funnel. Once separated from the stock tubing,and leaving only a small tabulation, the part was annealed in a furnaceat 570° C. for 20 minutes, and allowed to naturally cool to roomtemperature.

The closed top was finished with a 16 mm diameter hole cut close to oneside or off center from the center of the part. This allows thetransmembrane insert to be placed as close to the inside wall of theglass well (and hence the outer surface of the coil) as possible. Forconsistency, a wooden block was drilled to accept the glass welllower-diameter feature to a depth large enough to allow clearance forthe temporary tabulation. This wooden block was then positioned andclamped onto the stage of a drill press, in a position adjusted to wherethe outside diameter of the cutter was 2.5 mm off center from theoutside wall of the 14.6 mm×17 mm O.D. lower part of the well.Positioned in this manner, the cutter (made of brass) formed a hole offcenter in the desired position allowing the transmembrane insert to restagainst the wall of the lower portion of the glass well. The glass wellheld in the wooden jig had modeling clay applied to the outside of therim to contain 100 grit carborundum cutting powder slurry mixed withwater. The action of the brass mandrel turning against the flat glasssurface of the top of the well with the cutting compound slurryproceeded to grind through over approximately 15 to 20 minutes. Apecking action was employed to reintroduce new cutting compound into the“groove” being formed.

The bottom was permanently closed after cleaning the part to remove thecutting compound and modeling clay. The part was chucked into the glassworking lathe from the wider, flared end. As the part turned, it waswarmed before a small torch was applied to heat the glass to a suitableworking temperature allowing for the temporary tabulation to be removed.The part was then allowed to cool, before being turned in the oppositedirection and chucked again into the lathe to apply a final finish onthe 16 mm diameter opening on the wider end. Finishing the open, 16 mmdiameter end involved bringing the part back to a warmed conditionbefore polishing the ground surface left from grinding the opening withthe brass mandrel. Once warmed, a small hand torch was used to fuse thesurface of the cut a little at a time until the entire circumference ofthe opening was “fire” polished. Care was taken not to overheat thesurfaces so as to not distort any other part of the well. The part wasthen flame annealed to a point safe from cracking before finally beingoven annealed, as described earlier.

Analysis of induced electric fields in modified transmembrane assayexperiments: a time-dependent magnetic induction (∂{right arrow over(B)}/∂t) must be present in order to induce an electric field in anon-contact manner. Such an induced electric field can be producedeither by a constant magnitude magnetic field that is changing itsdirection versus time or by a magnetic field in a specific directionthat is changing its magnitude with respect to time, or both. In thisembodiment, the latter approach was used.

The 20 Vpp, 100 kHz sawtooth shaped voltage waveform (FIG. 2a ) imposedon the electromagnetic coil results in a time-dependent current flowthrough it. The current through the coil varies in time both inmagnitude and direction, and is a complicated function of the inductanceand intrinsic capacitance of the coil as well as its coupling with thefunction generator. Consequently, the resulting magnetic induction incylindrical coordinates, {right arrow over (B)}(r,z,t), and associatedvector potential {right arrow over (A)}(r,z,t) vary with time both inmagnitude and direction, where r and z are the radial and axialcoordinates measured from an origin located at one end of the coil alongits centerline. The induced electric field {right arrow over (E)}(r,z,t)can then be calculated from the vector potential, {right arrow over(A)}(r,z,t):

$\begin{matrix}{\overset{->}{E} = {- \frac{\partial\overset{->}{A}}{\partial t}}} & (1)\end{matrix}$

The time-dependent current through the coil can be measured using asense resistance (a smaller resistance) connected in series with thecoil in the circuit, and by measuring the time-dependent voltage dropacross the 1.25 Ωsense resistance (FIG. 13). Extreme care must be takenso as to ensure that no stray capacitances arising for example from BNCconnectors corrupt the measurement. One way to verify the measurement,is to connect the sense resistance upstream of the coil and ensure thatthe same current profile versus time is obtained as when the senseresistance is connected downstream of the coil. It is also important topoint out that use of a sense resistance for current measurement is onlyreliable at low values of the duty cycle (on the order of tens of kHz orlower) because of the unknown intrinsic coil capacitance which isdifficult to quantify at high values of the duty cycle (e.g. at 100 kHz)due to leakage.

The following methodology is used for calculating the induced electricfields relevant to the present invention. The current through theelectromagnetic coil is measured for an imposed sawtooth voltagewaveform of 20 Vpp at 1 kHz using a 1.25Ω sense resistance (FIG. 13). Acircuit element model (FIG. 14) is then used to predict the currentthrough the coil at 1 kHz, and validated against the current measurementusing the sense resistance at 1 kHz. The model is used to infer theintrinsic coil capacitance (FIG. 14), and then used to predict the coilconduction current for the experimental conditions where the imposed 20Vpp sawtooth shaped voltage waveform is applied at 100 kHz. Once thetime-varying current is calculated, the vector potential {right arrowover (A)}(r,z,t) is calculated using an analytical solution for thevector potential at a point given a circular current winding of a givendiameter at a specific location:

$\begin{matrix}{A_{\phi\; j} = {\frac{\mu_{0}I}{\pi}{\sqrt{\frac{a_{j}}{m_{j}r}}\left\lbrack {{\left( {1 - \frac{m_{j}}{2}} \right){K\left( m_{j} \right)}} - {E\left( m_{j} \right)}} \right\rbrack}}} & (2)\end{matrix}$where

${m_{j} = \frac{4a_{j}r}{\left\lbrack {\left( {a_{j} + r} \right)^{2} + \left( {z - l_{j}} \right)^{2}} \right\rbrack}},$where K(m_(j)) is the complete elliptic integral of the first kind,E(m_(j)) is the complete elliptic integral of the second kind, l is thecurrent through winding j, a_(i) is the radius of the j^(th) winding, ris the radial coordinate, z is the axial coordinate (with the origintaken along the centerline of the coil and at one end of the coil), andA_(ϕj) is the contribution to the vector potential at (r,z) at time tdue to current l(t) flowing in the j^(th) winding. By taking the coil tobe comprised of a perfectly stacked set of wire loops (windings) withdifferent diameters and carrying the same current, the vector potentialat any point in space can be obtained as the superposition of theindividual contributions from each loop of wire in the coil:

$\begin{matrix}{A_{\phi} = {\sum\limits_{j = 1}^{N}{\frac{\mu_{0}I}{\pi}{\sqrt{\frac{a_{j}}{m_{j}r}}\left\lbrack {{\left( {1 - \frac{m_{j}}{2}} \right){K\left( m_{j} \right)}} - {E\left( m_{j} \right)}} \right\rbrack}}}} & (3)\end{matrix}$where N is the total number of windings in the coil (35 layers×159windings per layer=5565). Note that in Eq. (3) the only time dependentquantity is the current l. The radial and axial components of magneticinduction are then calculated from:

$\begin{matrix}{B_{r} = {{- \frac{\partial A_{\phi}}{\partial z}} = {\sum\limits_{j = 1}^{N}{\frac{\mu_{0}I}{2\pi}{\frac{\left( {z - l_{j}} \right)}{r\sqrt{\left( {a_{j} + r} \right)^{2} + \left( {z - l_{j}} \right)^{2}}}\left\lbrack {{- {K\left( m_{j} \right)}} + {\left( \frac{a_{j}^{2} + r^{2} + \left( {z - l_{j}} \right)^{2}}{\left( {a_{j} - r} \right)^{2} + \left( {z - l_{j}} \right)^{2}} \right){E\left( m_{j} \right)}}} \right\rbrack}}}}} & (4) \\{B_{z} = {{\frac{A_{\phi}}{r} + \frac{\partial A_{\phi}}{\partial r}} = {\sum\limits_{j = 1}^{N}{\frac{\mu_{0}I}{2\pi}{\frac{1}{r\sqrt{\left( {a_{j} + r} \right)^{2} + \left( {z - l_{j}} \right)^{2}}}\left\lbrack {{K\left( m_{j} \right)} + {\left( \frac{a_{j}^{2} - r^{2} - \left( {z - l_{j}} \right)^{2}}{\left( {a_{j} - r} \right)^{2} + \left( {z - l_{j}} \right)^{2}} \right){E\left( m_{j} \right)}}} \right\rbrack}}}}} & (5)\end{matrix}$and the induced electric field is given by:

$\begin{matrix}{E_{\phi} = {{- \frac{\partial A_{\phi}}{\partial t}} = {{- \frac{\mu_{0}}{\pi}}\left( \frac{dI}{dt} \right){\sum\limits_{j = 1}^{N}{\sqrt{\frac{a_{j}}{m_{j}r}}\left\lbrack {{\left( {1 - \frac{m_{j}}{2}} \right){K\left( m_{j} \right)}} - {E\left( m_{j} \right)}} \right\rbrack}}}}} & (6)\end{matrix}$where

$m_{j} = {\frac{4a_{j}r}{\left\lbrack {\left( {a_{j} + r} \right)^{2} + \left( {z - l_{j}} \right)^{2}} \right\rbrack}.}$Note that the induced electric field E_(□) calculated from (6) varieswith the radial coordinate r and axial coordinate z. For the case ofrapidly changing transients, it is recommended that the derivative dl/dtin equation (6) be calculated using higher order accurate finitedifference formulae such as a fourth-order accurate finite differenceformula.

In the described embodiment, the current through the coil is measuredusing a sense resistance of 1.25Ω with the function generator supplyinga 20 Vpp sawtooth waveform at 1 kHz (FIG. 15). Also shown in the figureis the coil conduction current calculated using the circuit elementmodel (FIG. 14). The intrinsic coil capacitance was determined byparametric variation to be 30 nF using the measured values (at 1 kHz) of50.45Ω for the d.c. resistance and 14.25 mH for the inductance. Varyingthe intrinsic coil capacitance alters the magnitude of the spike whereasthe inductance and resistance together shift the bowl shaped profile forall other times in the period (FIG. 15). As can be seen, the agreementbetween prediction and measurement is excellent.

The circuit element model is used to predict the current at 100 kHzusing the same values of inductance, resistance, and capacitance at 1kHz. The resulting current as a function of time exhibits asymmetry overa period (FIG. 16). The induced electric field is proportional to dl/dt(equation (6)) and is therefore also asymmetric over any given period.

Analysis of induced electric fields in visualization of actin filaments:in the following embodiment, for the purpose of visualizing actinfilaments using phalloidin and fluorescence microscopy, the orientationof the coil is changed compared to the configuration used in thetransmembrane assay experiments. The electromagnetic coil used togenerate the induced electric fields in these methods also consists ofmultiple windings (18 layers, ˜67 turns per layer) of insulated 32 AWG(0.268 mm diameter with insulation or 0.202 mm diameter bare) wire. Theinner diameter of the coil is 14.2 mm, the outer diameter is 2.332 cm,and its length is 2.47 cm. Measurements of the coil resistance andinductance using an LCR meter (Extech Instruments Model 380193) yields24.58Ω and 12.17 mH, respectively, at 1 kHz. The coil is placed at thecenter of the holder with a standard 60 mm diameter culture plate on top(FIG. 17, FIG. 5a ). The physical characteristics of the coil (wiregage, diameter, number of turns, length, number of layers) given hereare for the methods and embodiments discussed herein. It is appreciatedthat these parameters as well as the duty cycle of the imposed voltage(which is 100 kHz for this embodiment) can all be changed depending onthe desired effects. It is important to ensure that the functiongenerator (Hewlett Packard 33120A used in the present experiments) isable to drive sufficient current through the coil. In a similar manner,the holder can also be easily modified to accommodate a multi-well plate(FIG. 12). Currents through the coil and the resulting magneticinductions and induced electric fields can be calculated as described byequations (4)-(6) in the previous section for a 20 Vpp sawtooth voltagewaveform at a duty cycle of 100 kHz (FIG. 17, FIGS. 5b-5d ).

Analysis of actin filament distribution: images obtained from phalloidinand fluorescence microscopy are imported into MATLAB (2014a, Mathworks,Inc., Massachusetts, U.S.A.). Individual cells are isolated andre-oriented so that their longest dimension is in the horizontaldirection. Intensities are then separated into red, green, and blue sothat the background and nuclei intensities may be filtered out and onlythe green fluorescence from the actin filaments is extracted. Actinfluorescence intensities are analyzed versus cell length (longerdimension being the length), and averaged. These post-processed imagesand average intensities for the isolated cells shown in FIG. 6, areshown in FIGS. 18-20.

Experimental results for “normal” breast epithelial cells (MCF-10A): inthe following described embodiment, experiments on combined chemotaxisand electrotaxis performed with MCF10A cells in the modifiedtransmembrane assay utilized the growth factor EGF in the lowercompartment of the modified transmembrane assay. After allowing 16 hoursof incubation in the modified transmembrane assay, the cells thatmigrated to the other side of the Transwell membrane in the top chamberwere stained with Hema 3 stain kit (Fisher Scientific, 122-911)according to the manufacturer's instructions. The stained cells werethen photographed with a Zeiss microscope attached to a camera. Themigrated cells were counted in five representative fields. As anillustration, representative fields are shown in FIG. 21. Data formigration of MCF-10A cells with and without growth factor EGF and withand without induced electric fields, is shown in FIG. 22. As can be seenfrom FIGS. 21-22, MCF-10A cells hardly migrate without the presence ofEGF (control in FIG. 22), and the presence of an electric field in thedirection of migration (“North” side) has no statistically significanteffect in this case in the absence of EGF (Coil North+E−EGF in FIG. 22).On the other hand, it can be seen that EGF strongly promotes migrationof MCF-10A cells (−E+EGF in FIG. 22) and the induced electric fieldhinders their migration (Coil North+E+EGF in FIG. 22) with statisticalsignificance (p=0.002) for −E+EGF versus Coil North+E+EGF in FIG. 22).

The glass wells illustrated in FIG. 7 are configured to accommodatecommercially available Transwell transmembrane inserts. The outercompartment and holder (FIG. 8) are designed so that the membrane (thebottom surface of the inner funnel) is as close as possible to the outersurface of the coil, to within 1 mm.

The holder is preferably fabricated using 3-D printing technology afterfirst developing a computer-aided design (CAD) drawing using thesoftware SolidWorks. The circular wells in the holder preferably haveunique dimensions based on the exact dimensions of each glass well (FIG.7). In one embodiment, the center channel of the holder allows the coilto be placed in the center so that there are three wells each on eitherside of the coil.

FIG. 9 illustrates representative fields (4 each) from the Transwelltransmembrane assay and the modified transmembrane assay with SCP2 cellsfixed and stained, showing how the cells are counted in one embodimentof the invention. The cells were allowed to migrate for 8 hours, andwere fixed and stained using Hema-3 stain kit according to themanufacturer's instructions. The number of migratory cells per membranewas then measured using light microscopy by counting the total number ofcells in each of five contiguous images taken at 20× magnification,spanning radially outward (five fields) from the coil. The counts wereused to determine the percentage of migration. Only a representative setof control images are shown as there was no statistically significantdifference between the control on the “North” and “South” sides.

FIG. 10 illustrates how the modified transmembrane assay with theTranswell membrane inserts reproduces cell migration observed in thepresently used multi-well plates with the same inserts. These cellmigration experiments were performed over a period of 8 hours on SCP2cells (N=3). No induced electric field was applied and the same media(0.1% FBS-DMEM) was used (p=0.993).

FIG. 10 illustrates one embodiment of a modified holder, coil, andculture plate used in the experiments to image actin filaments usingphalloidin and fluorescence microscopy. The holder is preferablyfabricated using 3-D printing technology after first developing acomputer-aided design (CAD) drawing using the software SolidWorks.

FIG. 12 illustrates how a modified assembly for accommodating a cultureplate may be altered for a 96 well multi-well plate. The holder ispreferably fabricated using 3-D printing technology after firstdeveloping a computer-aided design (CAD) drawing using the softwareSolidWorks.

FIG. 13 illustrates one embodiment of a circuit diagram showing the useof a sense resistor to measure the current through the coil. The coilhas a d.c. resistance, inductance, and intrinsic capacitance (FIG. 14).Consequently, measurement of the current in the circuit by placing thesense resistance downstream of the coil, and measuring the voltage dropyields the total current flow (sum of conduction and displacementcurrents through the coil). This measurement at 1 kHz allows theintrinsic capacitance to be inferred by comparing the measured voltagetrace across the sense resistance with a voltage trace predicted by acircuit element model that simulates the coil as a resistor in serieswith an inductor, both of which are in parallel with a capacitor (FIG.14). This intrinsic coil capacitance is then used to calculate theconduction current at 100 kHz, relevant for the electrotaxisexperiments. The current measurement described herein is sensitive tostray capacitances that can arise from coax connectors (such as tees)placed at the oscilloscope. Therefore, care must be exercised toeliminate such sources of stray capacitance. Ultimately, a check of themeasurement can be accomplished as the current measured with the sensecapacitance placed upstream of the coil should yield a similar currentas when the sense capacitance is placed downstream of the coil.

FIG. 14 illustrates one embodiment of a circuit diagram showing a modelused to predict the current through the coil. This circuit element modelis used to predict the total current through the coil at 1 kHz, and tocompare it with the current measurement using the sense resistance (FIG.13) at 1 kHz. This enables the intrinsic coil capacitance to be inferred(30 nF) by matching the prediction with measurement at 1 kHz. This valueof the intrinsic coil capacitance is then used to predict the conductioncurrent through the coil at the experimental duty cycle of 100 kHz.

FIG. 15 illustrates a chart showing the total current through theelectromagnetic coil used in the transmembrane assay experimentsdiscussed herein (measured in red, calculated in black) at a duty cycleof 1 kHz for a 20 Vpp sawtooth voltage waveform. By systematicallyvarying only the intrinsic coil capacitance until the prediction matchesthe measurement yields a value of 30 nF. The spike in the figure is dueto the displacement current passing through the coil capacitance. Thisinferred value of the intrinsic coil capacitance is then used to predictthe conduction current through the coil at 100 kHz.

FIG. 16 illustrates a chart showing predicted current (top) through theelectromagnetic coil used in the transmembrane assay experiments, at aduty cycle of 100 kHz for a 20 Vpp sawtooth voltage waveform, and itsderivative (bottom). It can be seen that the derivative of the currentthrough the coil is asymmetric over a single period of the duty cycle sothat the electric field is in the downward direction on the “South” and“North” sides of the coil for different durations (˜40% on the “South”side and ˜60% on the “North” side).

FIG. 17 illustrates a chart showing predicted current through theelectromagnetic coil used in the actin filament imaging experiments, ata duty cycle of 100 kHz for a 20 Vpp sawtooth voltage waveform. It canbe seen that the derivative of the current through the coil isapproximately symmetric over a single period of the duty cycle so thatthe electric field is in the leftward and rightward directions fordifferent durations on the culture plate (when viewed from the top)(FIGS. 5b-5e ).

FIGS. 18a and 18b illustrate charts showing the average intensity ofactin fluorescence versus length along isolated cells shown in the leftpanel of FIG. 6a . The actin cytoskeleton in SCP2 cells in the absenceof both EGF and induced electric fields is quantified here and averagedto show the distribution of fluorescence intensity versus length alongthe cell. Also shown in the upper right images of both panels (A) and(B) are the filtered images displaying only the actin cytoskeleton.

FIGS. 19a and 19b illustrate charts showing the average intensity ofactin fluorescence versus length along isolated cells shown in themiddle panel of FIG. 6a . The actin cytoskeleton in SCP2 cells in thepresence of EGF and without induced electric fields is quantified hereand averaged to show the distribution of fluorescence intensity versuslength along the cell. Also shown in the upper right images of bothpanels (A) and (B) are the filtered images displaying only the actincytoskeleton.

FIGS. 20a through 20c illustrate charts showing the average intensity ofactin fluorescence versus length along isolated cells shown in the rightpanel of FIG. 6a . The actin cytoskeleton in SCP2 cells in the presenceof both EGF and induced electric fields is quantified here and averagedto show the distribution of fluorescence intensity versus length alongthe cell. Also shown in the upper right images of panels (A), (B), and(C) are the filtered images displaying only the actin cytoskeleton.

FIG. 21 illustrates representative fields from the modifiedtransmembrane assay with a Transwell membrane with MCF-10A cells fixedand stained, showing how the cells are counted. In this embodiment, thecells were allowed to migrate for 16 hours, and were fixed and stainedusing Hema-3 stain kit according to the manufacturer's instructions. Thenumber of migratory cells per membrane was then measured using lightmicroscopy by counting the total number of cells in each of fivecontiguous images spanning radially outward (five fields) from the coil.The counts were used to determine the percentage of migration.

FIG. 22 illustrates a chart showing a summary of experimental results ofmigration of MCF-10A cells in the modified transmembrane assay showingthe effects of induced electric fields with and without the growthfactor EGF. These cell migration experiments were performed over aperiod of 16 hours on MCF-10A cells. These experiments were performed onthe same apparatus and under the same conditions as in FIG. 4. Column 1:Control without induced E fields or EGF in the modified transmembraneassay (N=2). Column 2: Effect of induced E fields on MCF-10 cells in theabsence of EGF on the “North” side of the modified transmembrane assay(N=2). Column 3: Control in the modified transmembrane assay with aTranswell insert, without induced E fields but in the presence of growthfactor EGF in the lower chamber (N=4). Column 4: Migration is hinderedon the “North” side of the coil in the presence of both EGF and inducedelectric fields (Column 3 versus Column 4: p=0.002), where for themajority (60%) of the 10 □s period, the induced E field is in thedirection of migration (i.e. directed downward) (N=4).

While certain embodiments of the present invention are described indetail above, the scope of the invention is not to be considered limitedby such disclosure, and modifications are possible without departingfrom the spirit of the invention as evidenced by the following claims:

What is claimed is:
 1. A method for controlling cell migration comprising the steps of: providing an electromagnetic coil having a first end and a second end; connecting the electromagnetic coil to a function generator; applying a time-varying voltage waveform to the electromagnetic coil, wherein the time-varying voltage waveform has a sharp drop off at its trailing edge and wherein the induced electric field is a rapidly time-varying magnetic field; inducing a time-varying electric field around the electromagnetic coil; placing the electromagnetic coil adjacent to, and without contacting, the location of cells; hindering the migration of the cells using the induced electric field.
 2. A method according to claim 1 further comprising the steps of: inducing eddy currents near the location of the cells; and varying the direction and spatial extent of the induced electric field enabling different cells to migrate at different times.
 3. A method according to claim 1, wherein the time-varying waveform is a sawtooth waveform.
 4. A method according to claim 1, wherein the time-varying waveform is a 20 volts peak to peak, 100 kHz sawtooth waveform with a 50 ns drop off at its trailing edge.
 5. A method according to claim 1, further comprising the step of: applying the induced electric field in a direction of cell migration.
 6. A method according to claim 1, further comprising the steps of: placing the electromagnetic coil in between a first row of a plurality of assay wells and second row of a plurality of assay wells; providing a plurality of well inserts having a porous membrane; placing one of the well inserts into each of the plurality of assay wells so that the wells are divided into a lower and upper compartment; placing a medium into each of the plurality of assay wells; placing a predetermined line of cancer cells into each of the assay wells; and allowing the predetermined lines of cancer cells to settle on top of the porous membranes.
 7. A method according to claim 6, further comprising the step of: introducing a predetermined chemokine into each of the assay wells.
 8. A method for controlling cancer cell migration comprising the steps of: providing an electromagnetic coil having a first end and a second end; connecting the electromagnetic coil to a function generator; applying a time-varying voltage waveform to the electromagnetic coil; selecting the diameter, shape and size of the coil so that the induced electric field is uniform over a desired region; inducing a time-varying electric field around the electromagnetic coil; placing the electromagnetic coil adjacent to, and without contacting, the location of cancer cells; and hindering migration of the cancer cells using the induced electric field.
 9. A method according to claim 8, wherein the time-varying waveform is a 20 volts peak to peak, 100 kHz sawtooth waveform with a 50 ns drop off at its trailing edge.
 10. A method according to claim 8, further comprising the step of varying the direction and spatial extent of the induced electric field enabling different cells to migrate at different times.
 11. A method according to claim 8, further comprising the steps of: placing the electromagnetic coil in between a first row of a plurality of assay wells and second row of a plurality of assay wells; providing a plurality of well inserts having a porous membrane; placing one of the well inserts into each of the plurality of assay wells so that the wells are divided into a lower and upper compartment; placing a medium into each of the plurality of assay wells; placing a predetermined line of cancer cells into each of the assay wells; and allowing the predetermined lines of cancer cells to settle on top of the porous membranes.
 12. A method according to claim 11, further comprising the steps of: taking an image of the porous membrane after the step of inducing a time-varying electric field; and quantifying metastatic potential of the predetermined lines of cancer cells.
 13. A method according to claim 8, further comprising the step of: orientating the placement of the electromagnetic coil so that the direction of the electric field is applied in a direction of migration of the cancer cells.
 14. A method according to claim 1, wherein the coil has multiple layers of windings with an outer diameter larger than an inner diameter.
 15. A method according to claim 8, wherein the coil has multiple layers of windings with an outer diameter larger than an inner diameter.
 16. A method according to claim 1, further comprising the step of selecting the diameter, shape and size of the coil to exert a particular value of the induced electric field at specific locations located radially from the coil.
 17. A method according to claim 8, further comprising the step of selecting the diameter, shape and size of the coil to exert a particular value of the induced electric field at specific locations located radially from the coil.
 18. A method according to claim 1, wherein the induced electric field is asymmetric over a duty cycle.
 19. A method according to claim 8, wherein the induced electric field is asymmetric over a duty cycle.
 20. A method according to claim 1, further comprising the steps of: measuring current through the coil using a sense resistance; predicting the current through the coil and comparing it to the measured current; predicting the coil conduction current for a predetermined voltage waveform at a higher frequency; calculating the vector potential; calculating the radial and axial components of magnetic induction; calculating the induced electric field; and using the calculated induced electric field to select a desired coil design.
 21. A method according to claim 8, further comprising the steps of: measuring current through the coil using a sense resistance; predicting the current through the coil and comparing it to the measured current; predicting the coil conduction current for a predetermined voltage waveform at a higher frequency; calculating the vector potential; calculating the radial and axial components of magnetic induction; calculating the induced electric field; and using the calculated induced electric field to select a desired coil design.
 22. A method according to claim 1, wherein the induced electric field has a magnitude on the order of 1 microvolt/cm or less.
 23. A method according to claim 8, wherein the induced electric field has a magnitude on the order of 1 microvolt/cm or less.
 24. A method according to claim 5, wherein the time-varying waveform induces an electric field in the direction of migration for a greater duration than in a direction opposite to the direction of migration.
 25. A method according to claim 13, wherein the time-varying sawtooth waveform induces an electric field in the direction of migration for a greater duration than in a direction opposite to the direction of migration.
 26. A method for controlling cell migration comprising the steps of: providing an electromagnetic coil having a first end and a second end; connecting the electromagnetic coil to a function generator; applying a time-varying voltage waveform to the electromagnetic coil; inducing a time-varying electric field around the electromagnetic coil, wherein the induced electric field has a magnitude on the order of 1 microvolt/cm or less; placing the electromagnetic coil adjacent to, and without contacting, the location of cells; and hindering the migration of the cells using the induced electric field.
 27. A method according to claim 26, wherein the time-varying waveform is a sawtooth waveform having a sharp drop off at its trailing edge.
 28. A method according to claim 26, further comprising the step of: applying the induced electric field in a direction of cell migration; and wherein the time-varying waveform induces an electric field in the direction of migration for a greater duration than in a direction opposite to the direction of migration.
 29. A method according to claim 26, further comprising the step of selecting the diameter, shape and size of the coil to exert a particular value of the induced electric field at specific locations located radially from the coil.
 30. A method according to claim 26, wherein the time-varying waveform is a 20 volts peak to peak, 100 kHz sawtooth waveform with a 50 ns drop off at its trailing edge; and wherein the induced electric field is a rapidly time-varying magnetic field. 